Multi-modal neural network for universal, online learning

ABSTRACT

In one embodiment, the present invention provides a neural network comprising multiple modalities. Each modality comprises multiple neurons. The neural network further comprises an interconnection lattice for cross-associating signaling between the neurons in different modalities. The interconnection lattice includes a plurality of perception neuron populations along a number of bottom-up signaling pathways, and a plurality of action neuron populations along a number of top-down signaling pathways. Each perception neuron along a bottom-up signaling pathway has a corresponding action neuron along a reciprocal top-down signaling pathway. An input neuron population configured to receive sensory input drives perception neurons along a number of bottom-up signaling pathways. A first set of perception neurons along bottom-up signaling pathways drive a first set of action neurons along top-down signaling pathways. Action neurons along a number of top-down signaling pathways drive an output neuron population configured to generate motor output.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation of U.S. Non-Provisional patentapplication Ser. No. 13/325,321 filed Dec. 14, 2011, the disclosure ofwhich is incorporated herein by reference.

GOVERNMENT RIGHTS

This invention was made with Government support under HR0011-09-C-0002awarded by Defense Advanced Research Projects Agency (DARPA). TheGovernment has certain rights in this invention.

BACKGROUND

The present invention relates to neuromorphic and synaptroniccomputation, and in particular, a multi-modal neural network foruniversal, online learning.

Neuromorphic and synaptronic computation, also referred to as artificialneural networks, are computational systems that permit electronicsystems to essentially function in a manner analogous to that ofbiological brains. Neuromorphic and synaptronic computation do notgenerally utilize the traditional digital model of manipulating 0s and1s. Instead, neuromorphic and synaptronic computation create connectionsbetween processing elements that are roughly functionally equivalent toneurons of a biological brain. Neuromorphic and synaptronic computationmay comprise various electronic circuits that are modeled on biologicalneurons.

In biological systems, the point of contact between an axon of a neuronand a dendrite on another neuron is called a synapse, and with respectto the synapse, the two neurons are respectively called pre-synaptic andpost-synaptic. The essence of our individual experiences is stored inconductance of the synapses. The synaptic conductance changes with timeas a function of the relative spike times of pre-synaptic andpost-synaptic neurons, as per spike-timing dependent plasticity (STDP).The STDP rule increases the conductance of a synapse if itspost-synaptic neuron fires after its pre-synaptic neuron fires, anddecreases the conductance of a synapse if the order of the two firingsis reversed.

BRIEF SUMMARY

In one embodiment, the present invention provides a neural networkcomprising multiple modalities. Each modality comprises multipleneurons. The neural network further comprises an interconnection latticefor cross-associating signaling between the neurons in differentmodalities. Each neuron generates a signal in response to input signalsfrom one or more other neurons via the interconnection lattice. Theinterconnection lattice comprises a plurality of reciprocal signalingpathways for directed information flow between different modalities. Theplurality of reciprocal signaling pathways comprises top-down signalingpathways and bottom-up signaling pathways configured for informationflow in a first direction and a second direction opposite to the firstdirection, respectively. Each bottom-up signaling pathway has areciprocal top-down signaling pathway, such that bottom-up signalingpathways for a first set of modalities influence top-down signalingpathways for a second set of modalities via learning rules.

In another embodiment, the present invention provides a neural networkcomprising a first set and a second set of neural nodes. Each node ofthe first set comprises multiple neuron populations including multipleneurons. Each node of the second set is a union of at least two nodes ofthe first set. The neural network further comprises an interconnectnetwork comprising multiple directed edges that connect neuron in nodesof the first set with neurons in nodes of the second set. Nodes of thefirst and second set are arranged in a lattice. A connected node of thesecond set exchanges signals with at least two nodes of the first setvia the interconnect network. Each neuron generates a firing signal inresponse to input signals from one or more other neurons via theinterconnect network.

In yet another embodiment, the present invention provides a methodcomprising interconnecting a plurality of neural nodes via aninterconnect network of multiple signaling pathways arranged in alattice. Interconnecting said plurality of neural nodes includesconnecting a plurality of first nodes in a first set of nodes with aplurality of second nodes in a second set of nodes. Each node generatesa signal in response to input signals received from one or more othernodes via the interconnect network. A connected node in the second setexchanging signals with at least two nodes in the first set via theinterconnect network.

In yet another embodiment, the present invention provides a computerprogram product on a computer-readable medium for cross-associatingsignaling in a neural network comprising a plurality of neural nodesconnected via an interconnect network. The interconnect networkcomprises bottom-up signaling pathways and top-down signaling pathwaysarranged in a lattice. Each node has a sensory-motor modality andgenerates a signal in response to input signals received from one ormore other nodes via the interconnect network.

These and other features, aspects and advantages of the presentinvention will become understood with reference to the followingdescription, appended claims and accompanying figures.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 illustrates an example structure of a neural module, inaccordance with an embodiment of the invention;

FIG. 2 illustrates a neural network circuit, in accordance with anembodiment of the invention;

FIG. 3 illustrates nodes arranged in an interconnection lattice, inaccordance with an embodiment of the invention;

FIG. 4 illustrates acyclic digraphs for each node in a lattice, inaccordance with an embodiment of the invention;

FIG. 5 illustrates a bottom-up digraph of the lattice, in accordancewith an embodiment of the invention;

FIG. 6 illustrates a lattice including a top-down digraph correspondingto a bottom-up digraph of the lattice, in accordance with an embodimentof the invention;

FIG. 7 illustrates a lattice including a combined perception-actiongraph, in accordance with an embodiment of the invention;

FIG. 8 illustrates a lattice including a combined perception-actiongraph, in accordance with another embodiment of the invention;

FIG. 9 illustrates a bijection between vertices, in accordance with anembodiment of the invention;

FIG. 10 illustrates neuron populations of vertices, in accordance withan embodiment of the invention;

FIG. 11 illustrates an example of synaptic connections between neuronpopulations, in accordance with an embodiment of the invention;

FIG. 12 illustrates another example of synaptic connections betweenneuron populations, in accordance with an embodiment of the invention;

FIG. 13 illustrates another example of neuron populations, in accordancewith an embodiment of the invention;

FIG. 14 illustrates yet another example of synaptic connections betweenneuron populations;

FIG. 15 illustrates an example neural network, in accordance with anembodiment of the invention;

FIG. 16 illustrates a neural network with an evaluation module, inaccordance with an embodiment of the invention;

FIG. 17 illustrates a neural network with an evaluation module, inaccordance with an embodiment of the invention;

FIG. 18 illustrates an evaluation module 70 of a neural network, inaccordance with an embodiment of the invention;

FIG. 19A illustrates an example of bijection between vertices, inaccordance with an embodiment of the invention;

FIG. 19B illustrates another example of bijection between vertices, inaccordance with an embodiment of the invention;

FIG. 20 illustrates an example of weights of the synaptic connectionsbetween neuron populations, in accordance with an embodiment of theinvention;

FIG. 21 illustrates another example of weights of the synapticconnections between neuron populations, in accordance with an embodimentof the invention;

FIG. 22A illustrates an example Hebbian learning rule, in accordancewith the present invention;

FIG. 22B illustrates an example anti-Hebbian learning rule, inaccordance with the present invention;

FIG. 23 illustrates a flowchart of an example process 800 for a lattice,in accordance with an embodiment of the invention;

FIG. 24 illustrates a flowchart of an example process 900 for a neuralnetwork, in accordance with an embodiment of the invention; and

FIG. 25 is a high level block diagram showing an information processingcircuit 300 useful for implementing one embodiment of the presentinvention.

DETAILED DESCRIPTION

The present invention relates to a multi-modal neural network foruniversal, online learning. In one embodiment, the present inventionprovides a neural network comprising multiple modalities, wherein eachmodality comprises multiple neurons. The neural network furthercomprises an interconnection lattice for cross-associating signalingbetween the neurons in the different modalities. Each neuron generates asignal in response to input signals from one or more other neurons viathe interconnection lattice.

The interconnection lattice comprises a plurality of reciprocalsignaling pathways for directed information flow between differentmodalities. The plurality of reciprocal signaling pathways comprisestop-down signaling pathways and bottom-up signaling pathways configuredfor information flow in a first direction and a second directionopposite to the first direction, respectively.

Each bottom-up signaling pathway has a reciprocal top-down signalingpathway, such that bottom-up signaling pathways for a first set ofmodalities influence top-down signaling pathways for a second set ofmodalities via learning rules. The bottom-up signaling pathways arearranged in an acyclic bottom-up digraph. The top-down signalingpathways are arranged in an acyclic top-down digraph, such that eachtop-down signaling pathway in the top-down digraph has a reciprocalbottom-up signaling pathway in the bottom-up digraph, and each actionneuron population along a top-down signaling pathway in the top-downdigraph corresponds to a perception neuron population along a reciprocalbottom-down pathway in the bottom-up digraph.

Each modality further includes a perception neuron population and anaction neuron population, such that each perception neuron has acorresponding action neuron. A perception neuron population at an inputperiphery of the neural network is designated as an input neuronpopulation configured to receive sensory input, and an action neuronpopulation at an output periphery of the neural network is designated asan output neuron population configured to generate motor output.

The interconnection lattice further includes a plurality of perceptionneuron populations along a number of bottom-up signaling pathways, and aplurality of action neuron populations along a number of top-downsignaling pathways. The input neuron population drives perceptionneurons along a number of bottom-up signaling pathways. A first set ofperception neurons along bottom-up signaling pathways drive a first setof action neurons along top-down signaling pathways. Action neuronsalong a number of top-down signaling pathways drive the output neuronpopulation.

Each perception neuron along a bottom-up signaling pathway is trainedusing a learning rule based on the firing events of said perceptionneuron and the firing events of the corresponding action neuron along areciprocal top-down signaling pathway. Each action neuron along atop-down signaling pathway is trained using a learning rule based on thefiring events of said action neuron and the firing events of thecorresponding perception neuron along a reciprocal bottom-up signalingpathway.

In another embodiment, the present invention provides a neural networkcomprising a first set and a second set of neural nodes. Each node ofthe first set comprises multiple neuron populations including multipleneurons. Each node of the second set is a union of at least two nodes ofthe first set. The neural network further comprises an interconnectnetwork comprising multiple directed edges that connect neuron in nodesof the first set with neurons in nodes of the second set. Nodes of thefirst and second set are arranged in a lattice. A connected node of thesecond set exchanges signals with at least two nodes of the first setvia the interconnect network. Each neuron generates a firing signal inresponse to input signals from one or more other neurons via theinterconnect network.

Neuron populations in a node are interconnected via multiple directededges arranged in an acyclic digraph, each edge comprising a signalingpathway in the interconnect network. The interconnect networkinterconnects said nodes via bottom-up signaling pathways arranged in anacyclic bottom-up digraph in the interconnect network, each bottom-upsignaling pathway including one or more neuron populations and directededges. A first neuron population in a first node is interconnected to asecond neuron population in a second node only if the second node is asuperset of the first node. The interconnect network furtherinterconnects said nodes via top-down signaling pathways arranged in anacyclic top-down digraph in the interconnect network, each top-downsignaling pathway including one or more neuron populations and directededges.

Each neuron population in the top-down digraph corresponds to a neuronpopulation in the bottom-up digraph. Each top-down signaling pathway inthe top-down digraph has a reciprocal bottom-up signaling pathway in thebottom-up digraph, wherein information flows along said top-downsignaling pathway in a first direction, and information flows along saidreciprocal bottom-up signaling pathway in a direction opposite of thefirst direction.

A neuron population at an input periphery of the neural network isdesignated as an input neuron population configured to receive sensoryinput, wherein the input neuron population drives neurons along a numberof bottom-up signaling pathways. A first set of neurons along bottom-upsignaling pathways drive a first set of neurons along top-down signalingpathways. A neuron population at an output periphery of the neuralnetwork is designated as an output neuron population configured togenerate motor output, wherein neurons along a number of top-downsignaling pathways drive the output neuron population.

Each neuron along a bottom-up signaling pathway is trained using alearning rule based on the firing events of said neuron and the firingevents of the corresponding neuron along a reciprocal top-down signalingpathway. Each neuron along a top-down signaling pathway is trained usinga learning rule based on the firing events of said neuron and the firingevents of the corresponding neuron along a reciprocal bottom-upsignaling pathway.

In yet another embodiment, the present invention provides a methodcomprising interconnecting a plurality of neural nodes via aninterconnect network of multiple signaling pathways arranged in alattice. Interconnecting said plurality of neural nodes includesconnecting a plurality of first nodes in a first set of nodes with aplurality of second nodes in a second set of nodes. Each node generatesa signal in response to input signals received from one or more othernodes via the interconnect network. A connected node in the second setexchanging signals with at least two nodes in the first set via theinterconnect network.

A node comprises one or more neuron populations interconnected viamultiple directed edges arranged in an acyclic digraph, wherein eachneuron population comprises one or more neurons, and each edge includesa signaling pathway in the interconnect network. Interconnecting saidplurality of neural nodes further includes interconnecting saidplurality of neural nodes via bottom-up signaling pathways arranged inan acyclic bottom-up digraph in the interconnect network, each bottom-upsignaling pathway including one or more neuron populations and directededges. Interconnecting said plurality of neural nodes further includesinterconnecting said plurality of neural nodes via top-down signalingpathways arranged in an acyclic top-down digraph in the interconnectnetwork, each top-down signaling pathway including one or more neuronpopulations and directed edges.

In yet another embodiment, the present invention provides a computerprogram product on a computer-readable medium for cross-associatingsignaling in a neural network comprising a plurality of neural nodesconnected via an interconnect network. The interconnect networkcomprises bottom-up signaling pathways and top-down signaling pathwaysarranged in a lattice. Each node has a sensory-motor modality andgenerates a signal in response to input signals received from one ormore other nodes via the interconnect network.

Embodiments of the present invention provide a computationalarchitecture representing a number of sensory and motor(“sensory-motor”) modalities of a neural network, wherein each modalitycomprises an input and an output neuron population such that each inputneuron corresponds to exactly one output neuron. The input population ofeach modality drives perception neurons along a number of bottom-uppathways and the output population is driven by action neurons along anumber of top-down pathways, where each bottom-up pathway has areciprocal top-down pathway and each perception neuron has acorresponding action neuron. Bottom-up pathways from several modalitiescan interact along an underlying lattice and can influence top-downpathways of other modalities. Each perception neuron is trained via theoutput of the corresponding action neuron in the reciprocal top-downpathway, and, conversely, each action neuron is trained via the outputof the corresponding perception neuron. The entire system maintainsstable activity levels via self-tuning and gain control. The resultingcomputational architecture is online, local, parallel, distributed, candeal with massive influx of data, can be adapted to work with spikingneurons, can extract deep features, and can solve problems ofunsupervised learning, supervised learning, and reinforcement learningwithin a single universal substrate of adaptation.

The term digital neuron as used herein represents an architectureconfigured to simulate a biological neuron. A digital neuron createsconnections between processing elements that are roughly functionallyequivalent to neurons of a biological brain. As such, a neuromorphic andsynaptronic computation comprising digital neurons according toembodiments of the invention may include various electronic circuitsthat are modeled on biological neurons. Further, a neuromorphic andsynaptronic computation comprising digital neurons according toembodiments of the invention may include various processing elements(including computer simulations) that are modeled on biological neurons.Although certain illustrative embodiments of the invention are describedherein using digital neurons comprising electronic circuits, the presentinvention is not limited to electronic circuits. A neuromorphic andsynaptronic computation according to embodiments of the invention can beimplemented as a neuromorphic and synaptronic architecture comprisingcircuitry, and additionally as a computer simulation. Indeed,embodiments of the invention can take the form of an entirely hardwareembodiment, an entirely software embodiment or an embodiment containingboth hardware and software elements.

An external two-way communication environment may supply sensory inputsand consume motor outputs. Digital neurons implemented usingcomplementary metal-oxide-semiconductor (CMOS) logic gates receive spikeinputs and integrate them. The neurons include comparator circuits thatgenerate spikes when the integrated input exceeds a threshold. In oneembodiment, weighted synaptic connections are implemented usingtransposable 1-bit static random-access memory (SRAM) cells, whereineach neuron can be an excitatory or inhibitory neuron. Each learningrule on each neuron axon and dendrite are reconfigurable.

FIG. 1 illustrates an example structure of a neural module 20, inaccordance with an embodiment of the invention. Each neural module 20comprises multiple neurons 1. For instance, the neural module 20comprises four neurons, neurons v^(g)↑t, v^(g)↓, v^(b)↑, and v^(b)↓.Each neuron 1 of a neural module 20 is classified as one of thefollowing four types of neurons: a perception neuron in a learning,bottom-up pathway; an action neuron in a learning, top-down pathway; aperception neuron in an unlearning, bottom-up pathway; and, an actionneuron in an unlearning, top-down pathway. In this specification, aneuron in a learning pathway is generally referred to as a good neuron.A neuron in an unlearning pathway is generally referred to as a badneuron.

In FIG. 1, the neuron v^(g)↑ is a good perception neuron in a learning,bottom-up pathway, the neuron v^(g)↓ is a good action neuron in alearning, top-down pathway, the neuron v^(b)↑ is a bad perception neuronin an unlearning, bottom-up pathway, and the neuron v^(b)↓ is a badneuron in an unlearning, top-down pathway.

FIG. 2 illustrates a neural network circuit 30, in accordance with anembodiment of the invention. The neural network circuit 30 comprises aplurality of neural modules 20, such as neural modules N1, N2, N3, N4,N5, and N6. Each neural module 20 comprises multiple neurons 1 (FIG. 1).The neural network circuit 30 further comprises a plurality of synapses(i.e., synaptic connections) 5 interconnecting the neural modules 20.Each synapse 5 interconnects a first neural module 20 to a second neuralmodule 20, thereby allowing bi-directional information flow between theneurons 1 in the first neural module 20 and the neurons 1 in the secondneural module 20.

The neural network circuit 30 may be used to implement a neural networkcircuit combining multiple sensory and motor modalities into onecomputational architecture. Sensory and motor modalities representbiological sensors and actuators (e.g., eyes, ears, hands), as well asnon-biological sensors and actuators (e.g., thermal sensors).

For instance, the neural modules 20 of the neural network circuit 30 maybe organized into multiple neural module sets 31, such as a first neuralmodule set 31 comprising the neural modules N1 and N2, a second neuralmodule set 31 comprising the neural modules N3 and N4, and a thirdneural module set 31 comprising the neural modules N5 and N6. Eachneural module set 31 represents a different sensory or motor modality(e.g., vision, auditory, etc.).

Each neural module set 31 may cross-associate with other neural modulesets 31. Specifically, a neural module 20 in one neural module set 31may be interconnected to another neural module 20 in another neuralmodule set 31. For instance, a synapse 5 interconnects the neural moduleN2 in the first neural module set 31 to the neural module N4 in thesecond neural module set 31. Another synapse 5 interconnects the neuralmodule N2 in the first neural module set 31 to the neural module N6 inthe third neural module set 31. As such, the first neural module set 31cross-associates with both the second and third neural module sets 31.

A neural network may be represented as an acyclic directed graph(“digraph”) comprising a set of vertices (i.e., nodes) and a set ofdirected edges. Each directed edge interconnects a sending vertex to areceiving vertex. In this specification, let G′=(V′, E′) generallydenote an acyclic digraph comprising a set of vertices V′ and a set ofdirected edges E′. Let sink(G′) denote a subset of vertices in V′ thathave no outgoing directed edges (i.e., do not send out outgoingconnections). Let source(G′) denote a subset of vertices in V′ that haveno incoming directed edges (i.e., do not receive incoming connections).

Neural modules from several sensory and motor modalities can interactalong an underlying interconnection lattice. Let L generally denote aninterconnection lattice that cross-associates multiple sensory and motormodalities. Let S₁, S₂, . . . , S_(m) generally denote the sensory andmotor modalities, where m is the total number of sensory or motormodalities that the lattice L cross-associates. Let S generally denote amodality of the lattice L.

Further, let S′ generally denote a set. For any set S′, let |S′| denoteits cardinality. L comprises non-empty subsets of F≡{S₁, S₂, . . . ,S_(m)}. Sets {S₁}, {S₂}, . . . {S_(m)} denote atomic sets of themodalities S₁, S₂, . . . , S_(m), respectively. Let A={{S₁}, {S₂}, . . ., {S_(m)}}, where A denotes the set of all atomic sets.

FIGS. 3-6 illustrate the stages of setting up an example interconnectionlattice 100, in accordance with an embodiment of the invention.

FIG. 3 illustrates nodes arranged in an interconnection lattice 100, inaccordance with an embodiment of the invention. The lattice 100cross-associates multiple sensory and motor modalities, such asmodalities S₁, S₂, and S₃. The lattice 100 comprises a first set ofnodes comprising multiple nodes 2, and a second set of nodes comprisingmultiple nodes 3. Each node 2 represents an atomic set that has asensory or motor modality. Specifically, a first node 2 represents anatomic set {S₁} having the modality S₁, a second node 2 represents anatomic set {S₂} having the modality S₂, and a third node 2 represents anatomic set {S₃} having the modality S₃.

Each node 3 represents a union of two or more nodes 2 (i.e., two or moreatomic sets). Specifically, a first node 3 represents a superset {S₁,S₂}that is the union of atomic sets {S₁} and {S₂}. A second node 3represents a superset {S₁,S₃} that is the union of atomic sets {S₁} and{S₃}. A third node 3 represents a superset {S₂,S₃} that is the union ofatomic sets {S₂} and {S₃}. Finally, a fourth node 3 represents asuperset {S₁, S₂, S₃} that is the union of atomic sets {S₁}, {S₂}, and{S₃}.

Each modality S of the lattice L may be represented by an acyclicdigraph G^(S). Let acyclic digraph G^(S)=(V^(S), E^(S)) where V^(S)denotes the set of vertices in G^(S), and E^(S) denotes the set ofdirected edges in G^(S). Let sink(G^(S)) denote a subset of vertices inV^(S) that have no outgoing edges (i.e., outgoing connections). Letsource (G^(S)) denote a subset of vertices in V^(S) that have noincoming edges (i.e., incoming connections).

If S∈A (i.e., set {S} is an atomic set), digraph G^(S) is non-empty and|source(G^(S))|=1. One of the vertices in V^(S) must be a source, andonly one of the vertices in V^(S) can be a source. If S∉A (i.e., set {S}is not an atomic set), digraph G^(S) may be empty.

FIG. 4 illustrates acyclic digraphs 4 for each node 2, 3 in the lattice100, in accordance with an embodiment of the invention. Each node 2, 3comprises multiple vertices interconnected via multiple directed edges10. The vertices and edges 10 of each node 2, 3 are arranged in anacyclic digraph 4.

Specifically, the first node 2 representing the atomic set {S₁} (FIG. 3)provides an acyclic digraph G^({S) ₁ ^(}) in FIG. 4. The digraph G^({S)₁ ^(}) is non-empty, comprising vertices V₁ ^({S) ₁ ^(}) and V₂ ^({S) ₁^(}). The digraph G^({S) ₁ ^(}) further comprises a directed edge 10interconnecting the vertex V₁ ^({S) ₁ ^(}) to the vertex V₂ ^({S) ₁^(}). The vertex V₁ ^({S) ₁ ^(}) in the digraph G^({S) ₁ ^(}) is asource vertex.

The second node 2 representing the atomic set {S₂} (FIG. 3) provides anacyclic digraph G^({S) ₂ ^(}) in FIG. 4. The digraph G^({S) ₂ ^(}) isnon-empty, comprising vertices V₁ ^({S) ₂ ^(}), V₂ ^({S) ₂ ^(}), V₃^({S) ₂ ^(}), and V₄ ^({S) ₂ ^(}). The digraph G^({S) ₂ ^(}) furthercomprises multiple directed edges 10 interconnecting the vertices in thedigraph G^({S) ₂ ^(}). Specifically, the vertex V₁ ^({S) ₂ ^(}) isinterconnected to the vertex V₂ ^({S) ₂ ^(}), the vertex V₁ ^({S) ₂ ^(})is interconnected to the vertex V₃ ^({S) ₂ ^(}), the vertex V₂ ^({S) ₂^(}) is interconnected to the vertex V₃ ^({S) ₂ ^(}), and the vertex V₃^({S) ₂ ^(}) is interconnected to the vertex V₄ ^({S) ₂ ^(}). The vertexV₁ ^({S) ₂ ^(}) in the digraph G^({S) ₂ ^(}) is a source vertex.

The third node 2 representing the atomic set {S₃} (FIG. 3) provides anacyclic digraph G^({S) ₃ ^(}) in FIG. 4. The digraph G^({S) ₃ ^(}) isnon-empty, comprising vertices V₁ ^({S) ₃ ^(}), V₂ ^({S) ₃ ^(}), and V₃^({S) ₃ ^(}). The digraph G^({S) ₃ ^(}) further comprises multipledirected edges 10 interconnecting the vertices in the digraph G^({S) ₃^(}). Specifically, the vertex V₁ ^({S) ₃ ^(}) is interconnected to thevertex V₂ ^({S) ₃ ^(}), and the vertex V₁ ^({S) ₃ ^(}) is interconnectedto the vertex V₃ ^({S) ₃ ^(}). The vertex V₁ ^({S) ₃ ^(}) in the digraphG^({S) ₃ ^(}) is a source vertex.

The first node 3 representing the atomic set {S₁,S₂} (FIG. 3) providesan acyclic digraph G^({S) ₁ ^(,S) ₂ ^(}) in FIG. 4. The digraph G^({S) ₁^(,S) ₂ ^(}) is a non-empty, comprising vertices V₁ ^({S) ₁ ^(S) ₂ ^(}),V₂ ^({S) ₁ ^(,S) ₂ ^(}), and V₃ ^({S) ₁ ^(,S) ₂ ^(}). The digraph G^({S)₁ ^(,S) ₂ ^(}) further comprises multiple directed edges 10interconnecting the vertices in the digraph G^({S) ₁ ^(,S) ₂ ^(}).Specifically, the vertex V₁ ^(,{S) ₁ ^(,S) ₂ ^(}) is interconnected tothe vertex V₃ ^({S) ₁ ^(,S) ₂ ^(}), and the vertex V₂ ^({S) ₁ ^(,S) ₂^(}) is interconnected to the vertex V₃ ^({S) ₁ ^(,S) ₂ ^(}).

The second node 3 representing the atomic set {S₁,S₃} (FIG. 3) providesan acyclic digraph G^({S) ₁ ^(,S) ₃ ^(}) in FIG. 4. The digraph G^({S) ₁^(,S) ₃ ^(}) is empty.

The third node 3 representing the atomic set {S₂,S₃} (FIG. 3) providesan acyclic digraph G^({S) ₂ ^(,S) ₃ ^(}) in FIG. 4. The digraph G^({S) ₂^(,S) ₃ ^(}) is a non-empty, comprising only the vertex V₁ ^({S) ₂ ^(,S)₃ ^(}).

Each digraph G^(S) may be arranged in an acyclic bottom-up digraph,wherein the bottom-up digraph comprises the vertices and edges of eachdigraph G^(S). Let G^(↑) generally denote a bottom-up digraph.G^(↑)=(V^(↑), E^(↑)), where V^(↑) comprises all vertices ∪_(S∈L)V^(S),and E^(↑) comprises all edges ∪_(S∈L)E^(S). Source vertices in G^(↑)comprise only the source vertices in the acyclic digraphs correspondingto the atomic sets, that is source(G^(↑))=∪_(S∈A)source(G^(S)).

FIG. 5 illustrates a bottom-up digraph 200 of the lattice 100, inaccordance with an embodiment of the invention. The lattice 100 furtherprovides said acyclic bottom-up digraph 200 including all vertices anddirected edges 10 of the digraphs G^({S) ₁ ^(}), G^({S) ₂ ^(}), G^({S) ₃^(}), G^({S) ₁ ^(,S) ₂ ^(}), G^({S) ₁ ^(,S) ₃ ^(}), G^({S) ₂ ^(,S) ₃^(}), and G^({S) ₁ ^(,S) ₂ ^(,S) ₃ ^(}). Specifically, the bottom-updigraph 200 includes the vertices V₁ ^({S) ₁ ^(}), V₂ ^({S) ₁ ^(}), V₁^({S) ₂ ^(}), V₂ ^({S) ₂ ^(}), V₃ ^({S) ₂ ^(}), V₄ ^({S) ₂ ^(}), V₁^({S) ₃ ^(}), V₂ ^({S) ₃ ^(}), V₃ ^({S) ₃ ^(}), V₁ ^({S) ₁ ^(,S) ₂ ^(}),V₂ ^({S) ₁ ^(,S) ₂ ^(}), V₃ ^({S) ₁ ^(,S) ₂ ^(}), and V₁ ^({S) ₂ ^(,S) ₃^(}), and all directed edges 10 of the digraphs G^({S) ₁ ^(}), G^({S) ₂^(}), G^({S) ₃ ^(}), G^({S) ₁ ^(,S) ₂ ^(}), G^({S) ₁ ^(,S) ₃ ^(}),G^({S) ₂ ^(,S) ₃ ^(}), and G^({S) ₁ ^(,S) ₂ ^(,S) ₃ ^(}).

The set of directed edges E^(↑) for the bottom-up digraph G^(↑) maycontain additional directed edges 10. Three constraints are providedbelow to ensure that G^(↑) is an acyclic digraph.

The first constraint is as follows: For 5, T∈L, a directed edge from avertex V_(i) ^(S) in G^(S) to another vertex V_(j) ^(T) in G^(T) canexist only if the set {S} is a strict subset of the set {T}.

Referring back to FIG. 5, the bottom-up digraph 200 further comprisesadditional directed edges 10. Each directed edge 10 interconnects avertex of a first node with a vertex of a second node, wherein the setrepresented by the first node is a subset of the set represented by thesecond node.

For example, the sets {S₁} and {S₂} are subsets of the set {S₁,S₂}. Afirst directed edge 10 interconnects the vertex V₂ ^({S) ₁ ^(}) to thevertex V₁ ^({S) ₁ ^(,S) ₂ ^(}), a second directed edge 10 interconnectsthe vertex V₁ ^({S) ₁ ^(}) to the vertex V₂ ^({S) ₁ ^(,S) ₂ ^(}), athird directed edge 10 interconnects the vertex V₃ ^({S) ₂ ^(}) to thevertex V₁ ^({S) ₁ ^(,S) ₂ ^(}), and a fourth directed edge 10interconnects the vertex V₄ ^({S) ₂ ^(}) to the vertex V₂ ^({S) ₁ ^(,S)₂ ^(}). Similarly, the sets {S₂} and {S₃} are subsets of the set{S₂,S₃}. A fifth directed edge 10 interconnects the vertex V₃ ^({S) ₂^(}) to the vertex V₁ ^({S) ₂ ^(,S) ₃ ^(}), a sixth directed edge 10interconnects the vertex V₂ ^({S) ₃ ^(}) to the vertex V₁ ^({S) ₂ ^(,S)₃ ^(}), and a seventh directed edge 10 interconnects the vertex V₃ ^({S)₃ ^(}) to the vertex V₁ ^({S) ₂ ^(,S) ₃ ^(}).

The second constraint is as follows: The only source vertices in G^(↑)are the source vertices in the acyclic digraphs corresponding to theatomic sets, that is source(G^(↑))=∪_(S∈A)source(G^(S)). For some S∈L,let V_(s) ^(S) denote a vertex in V^(S). Let S_(j) denote an atomic setthat is a subset of S, and let S_(i) denote an atomic set that is not asubset of S. For every vertex V_(s) ^(S) that is not a source vertex, apath from a source vertex to V_(s) ^(S) exists. There, however, can beno path from a source vertex in every atomic set S_(i) to V_(s) ^(S).

Referring back to FIG. 5, each set {S₁}, {S₂}, and {S₃} is an atomic setwith the source vertex V₁ ^({S) ₁ ^(}), V₁ ^({S) ₂ ^(}), and V₁ ^({S) ₃^(}), respectively. Vertices V₁ ^({S) ₁ ^(}), V₁ ^({S) ₂ ^(}), and V₁^({S) ₃ ^(}) are the only vertices in the bottom-up digraph 200 that donot have incoming directed edges. All other vertices in the bottom-updigraph 200 have incoming directed edges. As such, the source verticesfor the bottom-up digraph 200 comprise only the vertices V₁ ^({S) ₁^(}), V₁ ^({S) ₂ ^(}), and V₁ ^({S) ₃ ^(}). As illustrated in FIG. 5, apath exists from each source vertex V₁ ^({S) ₁ ^(}), V₁ ^({S) ₂ ^(}),and V₁ ^({S) ₃ ^(}) to the non-source vertices. For example, the firstdirected edge 10 in G^({S) ₁ ^(}) forms a path between the source vertexV₁ ^({S) ₁ ^(}) and the vertex V₂ ^({S) ₁ ^(}).

The third constraint is as follows: A vertex can be a sink in G^(↑) onlyif it is in G^(F). Alternatively, a vertex can be a sink in G^(↑) onlyif it is in G^(S) such that for every strict superset T of set S (i.e.,T⊃S) where sets S, T∈L, G^(T) is an empty acyclic digraph. Further,there must be at least one outgoing directed edge from every vertex inG^(S) that is not a sink to some vertex in G^(T), where T⊃S.

Referring back to FIG. 5, vertices V₃ ^({S) ₁ ^(,S) ₂ ^(}) and V₁ ^({S)₂ ^(,S) ₃ ^(}) are the only vertices in the bottom-up digraph 200 thatdo not have outgoing directed edges. All the other vertices in thebottom-up digraph 200 have outgoing directed edges. As such, the sinkvertices for the bottom-up digraph 200 comprise only the vertices V₃^({S) ₁ ^(,S) ₂ ^(}) and V₁ ^({S) ₂ ^(,S) ₃ ^(}). As illustrated in FIG.5, a path exists from each non-sink vertex in S to a sink vertex in T,where T⊃S. For example, the fifth directed edge 10 forms a path betweenthe non-sink vertex V₃ ^({S) ₂ ^(}) and the vertex V₁ ^({S) ₂ ^(,S) ₃^(}) where {S₂, S₃}⊃{S₂}.

For every S∈L, let U^(S) be a set such that every element u∈U^(S)corresponds to one and exactly one element in V^(S), and vice versa.Thus, for every S∈L, there is a bijection between U^(S) and V^(S). Letu≡P^(S)(v) generally denote the bijection.

For every G^(S), there is a corresponding acyclic digraph H^(S)=(U^(S),D^(S)) where, for u₁=P^(S)(v₁) and u₂=P^(S)(v₂), there is an edge fromu₁ to u₂ in D^(S) if and only if there is an edge from v₂ to v₁ inE^(S). Further, the bottom-up digraph G^(↑) has a corresponding top-downdigraph H_(↓)=(U^(↓), E^(↓)), where U^(↓) comprises all vertices∪_(S∈L)U^(S). As stated above, there is a bijection between U^(S) andV^(S) for every S∈L. Accordingly, there is a natural one-to-onecorrespondence between elements of U^(↓) and V^(↑). For every v∈V^(↑),let P(v) denote its corresponding element in U^(↓). For u₁=P(v₁) andu₂=P(v₂), there is an edge from u₁ to u₂ in E^(↓) if and only if thereis an edge from v₂ to v₁ in E^(↑). For every v∈G^(↑) that is a source,the bijection u=P(v) in H^(↓) is a sink. For every v∈G^(↑) that is asink, the bijection u=P(v) in H^(↓) is a source.

Therefore, each vertex in the top-down digraph H^(↓) corresponds to avertex in the bottom-up digraph G^(↑), and each directed edge 10 in thetop-down digraph H^(↓) corresponds to a directed edge 10 in thebottom-up digraph G^(↑). Information flows along a directed edge 10 inthe top-down digraph H^(↓) in a first direction, and information flowsalong a corresponding directed edge 10 in the bottom-up digraph in adirection opposite of the first direction.

FIG. 6 illustrates the lattice 100 including a top-down digraph 400corresponding to the bottom-up digraph 200, in accordance with anembodiment of the invention. The top-down digraph 400 comprises acyclicdigraphs H^({S) ₁ ^(}), and H^({S) ₂}, H^({S) ₃}, H^({S) ₁,S₂}, H^({S) ₁^(,S) ₃ ^(}), and H^({S) ₂ ^(,S) ₃} corresponding to the acyclicdigraphs G^({S) ₁ ^(}), G^({S) ₂}, G^({S) ₃}, G^({S) ₁ ^(,S) ₂ ^(}),G^({S) ₁ ^(,S) ₃ ^(}), and G^({S) ₂ ^(,S) ₃ ^(}) in the bottom-updigraph 200, respectively.

Specifically, the digraph H^({S) ₁ ^(}) comprises vertices U₁ ^({S) ₁^(}) and U₂ ^({S) ₁ ^(}) corresponding to the vertices V₁ ^({S) ₁ ^(})and V₂ ^({S) ₁ ^(}) in the digraph G^({S) ₁ ^(}), respectively. Thevertex V₁ ^({S) ₁ ^(}) is a source, whereas the vertex U₁ ^({S) ₁ ^(}),the bijection of V₁ ^({S) ₁ ^(}), is a sink. For every directed edge 10in the digraph G^({S) ₁}, there is a reciprocal directed edge 10 in thedigraph H^({S) ₁ ^(}). For example, a directed edge 10 interconnectingthe vertex U₂ ^({S) ₁ ^(}) to the vertex U₁ ^({S) ₁ ^(}) in the digraphH^({S) ₁ ^(}) corresponds to the directed edge 10 interconnecting thevertex V₁ ^({S) ₁ ^(}) to in the vertex V₂ ^({S) ₁ ^(}) in the digraphG^({S) ₁ ^(}).

The digraph H^({S) ₂ ^(}) comprises vertices U₁ ^({S) ₂ ^(}), U₂ ^({S) ₂^(}), U₃ ^({S) ₂ ^(}), and U₄ ^({S) ₂ ^(}) corresponding to the verticesV₁ ^({S) ₂ ^(}), V₂ ^({S) ₂ ^(}), V₃ ^({S) ₂ ^(}), and V₄ ^({S) ₂ ^(})in the digraph G^({S) ₂ ^(}), respectively. The vertex V₁ ^({S) ₂ ^(})is a source, whereas the vertex U₁ ^({S) ₂ ^(}), the bijection of V₁^({S) ₂ ^(}), is a sink. For every directed edge 10 in the digraphG^({S) ₂ ^(}), there is a reciprocal directed edge 10 in the digraphH^({S) ₂ ^(}). For example, a directed edge 10 interconnecting thevertex U₂ ^({S) ₂ ^(}) to the vertex U₁ ^({S) ₂ ^(}) in the digraphH^({S) ₂ ^(}) corresponds to the directed edge 10 interconnecting thevertex V₁ ^({S) ₂ ^(}) to the vertex V₂ ^({S) ₂ ^(}) in the digraphG^({S) ₂ ^(}).

The digraph H^({S) ₃ ^(}) comprises vertices U₁ ^({S) ₃}, U₂{S₃}, and U₃^({S) ₃ ^(}) corresponding to the vertices V₁ ^({S) ₃ ^(}), V₂ ^({S) ₃^(}), and V₃ ^({S) ₃ ^(}) in the digraph G^({S) ₃ ^(}), respectively.The vertex V₁ ^({S) ₃ ^(}) is a source, whereas the vertex U₁ ^({S) ₃^(}), the bijection of V₁ ^({S) ₃ ^(}), is a sink. For every directededge 10 in the digraph G^({S) ₃ ^(}), there is a reciprocal directededge 10 in the digraph H^({S) ₃ ^(}). For example, a directed edge 10interconnecting the vertex U₂ ^({S) ₃ ^(}) to the vertex U₁ ^({S) ₃ ^(})in the digraph H^({S) ₃ ^(}) corresponds to the directed edge 10interconnecting the vertex V₁ ^({S) ₃ ^(}) to the vertex V₂ ^({S) ₃ ^(})in the digraph G^({S) ₃ ^(}).

The digraph H^({S) ₁ ^(,S) ₂ ^(}) comprises vertices U₁ ^({S) ₁ ^(,S) ₂^(}), U₂ ^({S) ₁ ^(,S) ₂ ^(}), and U₃ ^({S) ₁ ^(,S) ₂ ^(}) correspondingto the vertices V₁ ^({S) ₁ ^(,S) ₂ ^(}), V₂ ^({S) ₁ ^(,S) ₂ ^(}), and V₃^({S) ₁ ^(,S) ₂ ^(}) in the digraph G^({S) ₁ ^(,S) ₂ ^(}), respectively.The vertex V₃ ^({S) ₁ ^(,S) ₂ ^(}) is a sink, whereas the vertex U₃^({S) ₁ ^(,S) ₂ ^(}), the bijection of V₃ ^({S) ₁ ^(,S) ₂ ^(}), is asource. For every directed edge 10 in the digraph G^({S) ₁ ^(,S) ₂ ^(}),there is a reciprocal directed edge 10 in the digraph H^({S) ₁ ^(,S) ₂^(}). For example, a directed edge 10 interconnecting the vertex U₃^({S) ₁ ^(,S) ₂ ^(}) to the vertex U₁ ^({S) ₁ ^(,S) ₂ ^(}) in thedigraph H^({S) ₁ ^(,S) ₂ ^(}) corresponds to the directed edge 10interconnecting the vertex V₁ ^({S) ₁ ^(,S) ₂ ^(}) to the vertex V₃^({S) ₁ ^(,S) ₂ ^(}) in the digraph G^({S) ₁ ^(,S) ₂ ^(}).

Like the digraph G^({S) ₁ ^(,S) ₃ ^(}), the digraph H^({S) ₁ ^(,S) ₃^(}) is an empty digraph.

The digraph H^({S) ₂ ^(,S) ₃ ^(}) comprises a vertex U₁ ^({S) ₂ ^(,S) ₃^(}) corresponding to the vertex V₁ ^({S) ₂ ^(,S) ₃ ^(}) in the digraphG^({S) ₂ ^(,S) ₃ ^(}), respectively. The vertex V₁ ^({S) ₂ ^(,S) ₃ ^(})is a sink, whereas the vertex U₁ ^({S) ₂ ^(,S) ₃ ^(}), the bijection ofV₁ ^({S) ₂ ^(,S) ₃ ^(}), is a source.

The top-down digraph 400 further comprises additional directed edges 10.Specifically, for every directed edge 10 in the bottom-up digraph 200,there is a reciprocal directed edge 10 in the top-down digraph 400. Forexample, a directed edge 10 interconnecting the vertex U₁ ^({S) ₁ ^(,S)₂ ^(}) in the digraph H^({S) ₁ ^(,S) ₂ ^(}) to the vertex U₂ ^({S) ₁^(}) in the digraph H^({S) ₁ ^(}) corresponds to the directed edge 10interconnecting the vertex V₂ ^({S) ₁ ^(}) in the digraph G^({S) ₁ ^(})to the vertex V₁ ^({S) ₁ ^(,S) ₂ ^(}) in the diagraph G^({S) ₁ ^(,S) ₂^(}).

Vertices in the bottom-up digraph G^(↑) are interconnected via thedirected edges 10 to form bottom-up signaling pathways along whichinformation flows in a first direction. Vertices in the top-down digraphH^(↓) are interconnected via the directed edges 10 to form top-downsignaling pathways along which information flows in a direction oppositeto the first direction. The bottom-up digraph G^(↑) and the top-downdigraph H^(↓) may be connectable to provide a combined acyclicperception-action G=(V, E), where V=V^(↑) U^(↓) and E contains all thedirected edges E^(↑) E^(↓).

FIG. 7 illustrates the lattice 100 including a combinedperception-action graph 500, in accordance with an embodiment of theinvention. The perception-action graph 500 comprises all vertices in thebottom-up digraph 200 and the top-down digraph 400. Theperception-action graph 500 further comprises all directed edges 10 inthe bottom-up digraph 200 and the top-down digraph 400.

The set of edges E of the perception-action graph G may containadditional directed edges 10. Three constraints are provided below toensure that G is an acyclic digraph, and that for every directed edge 10interconnecting a vertex V to a vertex u, there is a reciprocal directededge interconnecting a vertex P(u) to a vertex P(v), where the verticesv, u, P(v), P(u)∈G.

The first constraint is as follows: Every vertex in sink(G^(↑)) musthave an outgoing directed edge, and every vertex in source(H^(↓)) musthave an incoming directed edge. Let source(G)=source(G^(↑)), and letsink(G)=sink(H^(↓)).

As described above, the sink vertices in the bottom-up digraph 200 arethe vertices V₃ ^({S) ₁ ^(,S) ₂ ^(}) and V₁ ^({S) ₂ ^(,S) ₃ ^(}), andthe source vertices in the top-down digraph 400 are the vertices U₃^({S) ₁ ^(,S) ₂ ^(}) and U₁ ^({S) ₂ ^(,S) ₃ ^(}). Referring back to FIG.7, each vertex V₃ ^({S) ₁ ^(,S) ₂ ^(}) and V₁ ^({S) ₂ ^(,S) ₃ ^(}) inthe bottom-up digraph 200 now has an outgoing directed edge 10.Specifically, a directed edge 10 interconnects the vertex V₃ ^({S) ₁^(,S) ₂ ^(}) to the vertex U₂ ^({S) ₃ ^(}), and a directed edge 10interconnects the vertex V₁ ^({S) ₂ ^(,S) ₃ ^(}) to the vertex U₂ ^({S)₁ ^(}). Each vertex U₃ ^({S) ₁ ^(,S) ₂} and U₁ ^({S) ₂ ^(,S) ₃ ^(}) inthe top-down digraph 400 now has an incoming directed edge 10.Specifically, a directed edge 10 interconnects the vertex V₂ ^({S) ₃^(}) to the vertex U₃ ^({S) ₁ ^(,S) ₂ ^(}), and a directed edge 10interconnects the vertex V₂ ^({S) ₁ ^(}) to the vertex U₁ ^({S) ₂ ^(,S)₃ ^(}).

The source vertices in the perception-action graph 500 are the verticesV₁ ^({S) ₁ ^(}), V₁ ^({S) ₂ ^(}), and V₁ ^({S) ₃ ^(}). The sink verticesin the perception-action graph 500 are the vertices U₁ ^({S) ₁ ^(}), U₁^({S) ₂}, and U₁ ^({S) ₃ ^(}).

The second constraint is as follows: For a vertex V∈V^(S), where V^(S)V^(↑), and for a vertex u∈U^(T), where U^(T) V_(↓), v and u areconnectable if S∩T=0. If v and u are connectable, then E may contain apair of directed edges 10 from v to u and from P(v) to P⁻¹(u). Forexample, referring back to FIG. 7, P(V₂ ^({S) ₁ ^(})) and P⁻¹(U₁ ^({S) ₂^(,S) ₃ ^(})) are the vertices U₂ ^({S) ₁ ^(}) and V₁ ^({S) ₂ ^(,S) ₃^(}), respectively. The directed edge 10 interconnecting the vertex V₁^({S) ₂ ^(,S) ₃ ^(}) to the vertex U₂ ^({S) ₁ ^(}) has a reciprocaldirected edge 10 interconnecting the vertex V₂ ^({S) ₁ ^(}) to thevertex U₁ ^({S) ₂ ^(,S) ₃ ^(}). Similarly, P(V₃ ^({S) ₁ ^(,S) ₂}) andP⁻¹(U₂ ^({S) ₃}) are the vertices U₃ ^({S) ₁ ^(,S) ₂ ^(}) and V₂ ^({S) ₃^(}), respectively. The directed edge 10 interconnecting the vertex V₃^({S) ₁ ^(,S) ₂ ^(}) to the vertex U₂ ^({S) ₃ ^(}) has a reciprocaldirected edge 10 interconnecting the vertex V₂ ^({S) ₃ ^(}) to thevertex U₃ ^({S) ₁ ^(,S) ₂ ^(}). This second constraint ensures thatinformation arising from a source vertex never feedbacks into itself.Thus, for prediction purposes, the prediction of each modality can bebased other modalities but not itself.

In one embodiment, the third constraint is as follows: To enableestimation (i.e., auto-association), a vertex V∈V^(S) is equated to avertex P(V)∈U^(S), where V^(S) V^(↑), and U^(S) U^(↓).

FIG. 8 illustrates the lattice 100 including the combinedperception-action graph 500, in accordance with another embodiment ofthe invention. To equate the vertex V₃ ^({S) ₁ ^(,S) ₂ ^(}) to thevertex U₃ ^({S) ₁ ^(,S) ₂} (i.e., P(V₃ ^({S) ₁ ^(,S) ₂})), output of thevertex V₃ ^({S) ₁ ^(,S) ₂ ^(}) is copied to the vertex U₃ ^({S) ₁ ^(,S)₂ ^(}). Similarly, to equate the vertex V₁ ^({S) ₂ ^(,S) ₃ ^(}) to thevertex U₁ ^({S) ₂ ^(,S) ₃ ^(}) (i.e., P(V₁ ^({S) ₂ ^(,S) ₃ ^(}))),output of the vertex V₁ ^({S) ₂ ^(,S) ₃ ^(}) is copied to the vertex U₁^({S) ₂ ^(,S) ₃ ^(}).

In another embodiment, the third constraint is as follows: A vertexV∈V^(S) is connectable to vertex u∈U^(T), where V^(S) V^(↑), U^(T)V^(↓), and S=T. If v and u are connectable, then E may contain a pair ofdirected edges from v to u and from P(v) to P⁻¹(u).

FIG. 9 illustrates the bijection between vertices, in accordance with anembodiment of the invention. As described above, for every directed edgeinterconnecting a vertex v to a vertex u, there is a reciprocal directededge interconnecting a vertex P(u) to a vertex P(v), where the verticesv, u, P(v), P(u)∈G.

Using the perception-action graph G described above, embodiments of aneural network substrate (“neural network”) suitable for supervised andunsupervised learning are now disclosed herein below. Every vertexV∈V^(↑) (i.e., a vertex in the bottom-up digraph G^(↑)) comprises aneuron population of perception neurons generally denoted as N(v). Everyvertex P(v)∈V^(↓) (i.e., a vertex in the top-down digraph H^(↓))comprises another neuron population of action neurons generally denotedas N(P(v)). Each directed edge 10 interconnecting a sending vertex to areceiving vertex comprises multiple synaptic connections 5 such that aneuron in a neuron population corresponding to the receiving vertexreceives synaptic connections from a subset of neurons in a neuronpopulation corresponding to the second vertex.

FIG. 10 illustrates neuron populations of vertices, in accordance withan embodiment of the invention. For any vertex V∈V^(↑), the vertex vcomprises a neuron population including multiple neurons 1, wherein theneurons 1 are perception neurons. The bijection of v, that isP(v)∈V^(↓), similarly comprises another neuron population includingmultiple neurons 1, wherein the neurons 1 are action neurons. The totalnumber of neurons 1 in the vertex v is the same as the total number ofneurons in the vertex P(v). Each neuron in the vertex v corresponds toexactly one neuron in the vertex P(v).

FIG. 11 illustrates an example of synaptic connections 5 between neuronpopulations, in accordance with an embodiment of the invention. For adirected edge 10 (FIG. 9) interconnecting a vertex v in G to a vertex uin G, every neuron 1 in the vertex u receives some synaptic connections5 from a set of neurons 1 in the vertex v. Each synaptic connection 5has a plastic, adaptive weight.

In one embodiment, every neuron 1 in the vertex u receives synapticconnections 5 from every neuron 1 in the vertex v. In anotherembodiment, every neuron in the vertex u receives synaptic connections 5from a subset of neurons in the vertex v. In yet another embodiment,every neuron in the vertex u receives connections from a random subsetof neurons in the vertex v.

Similarly, for the reciprocal directed edge 10 (FIG. 9) interconnectinga vertex P(u) to a vertex P(v), every neuron in the vertex P(v) receivessome synaptic connections 5 from a set of neurons 1 in the vertex P(u).The synaptic connections 5 between the vertex v and the vertex u neednot be symmetric with the synaptic connections 5 between the vertex P(u)and the vertex P(v).

In a neural network suitable for supervised and unsupervised learning,weights of the synaptic connections 5 are first initialized. Activationthen propagates in the neural network as follows: In every epoch (e.g.,time step), training patterns are presented to neurons 1 in all or somesource vertices. The neurons 1 in the source vertices are perceptionneurons. As source vertices are vertices at an input periphery of theneural network, the neurons 1 in the source vertices are designated asinput neurons.

Other neurons 1 corresponding to non-source vertices then determinewhether to emit a firing signal only after all the input neurons havedetermined whether to emit a firing signal. Activation is propagatedthrough the neural network until all neurons 1 have fired. Since theneural network is acyclic, there can be no deadlock, and every neuron 1will eventually fire.

In one embodiment, every neuron 1 is trained according to perceptionlearning rules. Specifically, every neuron 1 has a target output. Forevery perception neuron 1 in a vertex v, the target output is simply theoutput of the corresponding action neuron 1 in the vertex P(v), and viceversa. In another embodiment, Winnow learning rules or its variants maybe used for training the neurons 1.

FIG. 12 illustrates another example of synaptic connections 5 betweenneuron populations, in accordance with an embodiment of the invention.As described above, if there is a directed edge 10 (FIG. 9)interconnecting a vertex v in G to a vertex u in G, then every neuron inthe vertex u receives some synaptic connections 5 from a set of neurons1 in the vertex v. Unlike FIG. 10, the synaptic connections 5 betweenthe vertex v and the vertex u are symmetric with the synapticconnections 5 between the vertex P(u) and the vertex P(v). For asynaptic connection 5 from a first neuron 1 in the vertex v to a secondneuron 1 in the vertex u, there is a reciprocal synaptic connection 5from a third neuron 1 in the vertex P(u) to a fourth neuron 1 in thevertex P(v), where the fourth neuron corresponds to the first neuron andthe third neuron corresponds to the second neuron.

In one embodiment, each synaptic connection 5 has an adaptive, plasticweight. In another embodiment, the synaptic connection 5 interconnectingthe first neuron to the second neuron has the same weight as thereciprocal synaptic connection 5 interconnecting the third neuron to thefourth neuron.

In one embodiment, the neurons 1 are spiking neurons. For spikingneurons, an example learning rule is described as follows: If aperception neuron n along a bottom-up pathway fires, a spike-timingdependent Hebbian learning function may be applied between the lastfiring time of the corresponding action neuron P(n) along acorresponding top-down pathway and the last firing times of pre-synapticneurons to the neuron n (i.e., the neurons that send out outgoingsynaptic connections 5 to the neuron n). Similarly, if an action neuronm along a top-down pathway fires, a spike-timing dependent Hebbianlearning function may be applied between the last firing time of thecorresponding perception neuron P⁻¹(m) along the corresponding bottom-uppathway and the respective last firing times of the pre-synaptic neuronsto the neuron m (i.e., the neurons that send out outgoing synapticconnections 5 to the neuron m).

Other learning rules for the spiking neurons may also be used. In oneembodiment, the weight of each synaptic connection 5 cannot be negative.In another embodiment, the weight of each synaptic connection 5 may benegative.

FIG. 13 illustrates another example of neuron populations, in accordancewith an embodiment of the invention. In one embodiment, for every vertexV∈V in the perception-action graph G, vertices v^(g) and v^(b) areprovided. Each vertex V^(g) comprises a neuron population comprisingmultiple neurons 1, wherein each neuron 1 is a good perception neuron.Each vertex v^(b) comprises another neuron population comprisingmultiple neurons 1, wherein each neuron 1 is a bad perception neuron.The total number of neurons 1 in the vertex v^(g) is the same as thetotal number of neurons in the vertex v^(b) such that each neuron in thevertex v^(g) corresponds to exactly one neuron in the vertex v^(g).

The bijection of v^(g), that is the vertex P(v^(g))∈V, comprises anotherneuron population comprising multiple neurons 1, wherein each neuron isa good action neuron. The bijection of v^(b), that is the vertexP(v^(b))∈V, comprises another neuron population comprising multipleneurons 1, wherein each neuron is a bad action neuron. The total numberof neurons 1 in the vertex P(v^(g)) is the same as the total number ofneurons in the vertex P(v^(b)) such that each neuron in the vertexP(v^(g)) corresponds to exactly one neuron in the vertex P(v^(g)). Assuch, there will be equal number of neurons 1 in each vertex v^(g),v^(b), P(v^(g)), and P(v^(b)).

FIG. 14 illustrates yet another example of synaptic connections 5between neuron populations, in accordance with an embodiment of theinvention. Let n and m generally denote a neuron 1 in the vertex v^(g)and a neuron 1 in the vertex u^(g), respectively. For every synapticconnection 5 with a weight w interconnecting a neuron n of the vertexv^(g) to a neuron m of the vertex u^(g), there is a synaptic connection5 with the same weight w interconnecting a neuron corresponding to n inthe vertex v^(b) to a neuron corresponding to m in the vertex u^(b).Further, there are reciprocal synaptic connections between the vertexP(u^(g)) and the vertex P(v^(g)) and the vertex P(u^(b)) and the vertexP(v^(b)). The reciprocal synaptic connections 5 have the same weight x.

FIG. 15 illustrates an example neural network 600, in accordance with anembodiment of the invention. There must be at least one sensory modalityin a neural network. The neural network 600 utilizes the lattice 100(FIG. 7) to interconnect the motor modality S₃ and the sensorymodalities S₁ and S₂. Each vertex provides vertices v^(g) and v^(b)(FIG. 13) comprising a population of good neurons (G) and a populationof bad neurons (B), respectively. For each source vertex in an acyclicdigraph representing a sensory modality, good neurons in said sourcevertex receive sensory input for the sensory modality. As illustrated inFIG. 15, the good neurons in the source vertices V₁ ^({S) ₁ ^(}) and V₁^({S) ₂ ^(}) are configured to receive sensory input. For each sinkvertex in an acyclic digraph representing a motor modality, good neuronsin said sink vertex are configured to generate motor output. Asillustrated in FIG. 15, the good neurons in the sink vertex U₁ ^({S) ₃^(}) are configured to generate motor output.

FIG. 16 illustrates the neural network 600 with an evaluation module 70,in accordance with an embodiment of the invention. In anotherembodiment, the neural network 600 further comprises said evaluationmodule 70. For each sink vertex in an acyclic digraph representing amotor modality, motor output of the good neurons in said sink vertex areforwarded to the evaluation module 70. As illustrated in FIG. 16, motoroutput of the good neurons in the sink vertex U₁ ^({S) ₃ ^(}) areforwarded to the evaluation module 70. In one example implementation,each motor modality has its own corresponding evaluation module 70. Inanother example implementation, the evaluation module 70 receives inputfrom multiple motor modalities.

FIG. 17 illustrates the neural network 600 with the evaluation module70, in accordance with an embodiment of the invention. The evaluationmodule 70 determines if the motor output received from the good neuronsin the sink vertex is good or bad. If the motor output is good, theevaluation module 70 forwards the good motor output to the good neuronsin the corresponding source vertex of the motor modality. If the motoroutput is bad, the evaluation module 70 forwards the bad motor output tothe bad neurons in the corresponding source vertex of the motormodality. As illustrated in FIG. 17, good motor output of the goodneurons in the sink vertex U₁ ^({S) ₃ ^(}) is forwarded to the goodneurons in the corresponding source vertex V₁ ^({S) ₃ ^(}). Bad motoroutput of the good neurons in the sink vertex U₁ ^({S) ₃ ^(}) isforwarded to the bad neurons in the corresponding source vertex V₁ ^({S)₃ ^(}).

FIG. 18 illustrates the evaluation module 70 of the neural network 600(FIG. 17), in accordance with an embodiment of the invention. If themotor output of the neurons in the vertex P(v^(g)) is good, theevaluation module 70 feeds the good motor output to the neurons in thecorresponding source vertex v^(g), and a zero input to the neurons inthe corresponding source vertex v^(b). If the motor output of theneurons in the vertex P(v^(g)) is bad, the evaluation module 70 feedsthe bad motor output to the neurons in the corresponding source vertexv^(b), and a zero input to the neurons in the corresponding sourcevertex v^(g). Deadlock in activation propagation is thus prevented.

FIG. 19A illustrates an example of bijection between vertices, inaccordance with an embodiment of the invention. In one embodiment, everygood neuron is trained according to a perception learning rule.Specifically, every good neuron has a target output. For every goodperception neuron in the bottom-up digraph, the target output is simplythe output of the corresponding good action neuron in the top-downdigraph, and also the complement of the output of the corresponding badaction neuron in the top-down digraph.

Similarly, for every good action neuron in the top-down digraph, thetarget output is simply the output of the corresponding bad perceptionneuron in the bottom-up digraph, and also the complement of the outputof the corresponding bad perception neuron in the bottom-up digraph. Inanother embodiment, a Winnow learning rule or its variants may also beused.

For bad every neuron, there is no associated learning. Bad neurons aresimply used to train good neurons in counter path.

FIG. 19B illustrates another example of bijection between vertices, inaccordance with an embodiment of the invention.

In both FIGS. 19A and 19B, good perception neurons in the u^(g) vertexare trained to approximate good action neurons in the P(u^(g)) vertexand not to approximate bad action neurons in the P(u^(b)) vertex. If aneuron in the u^(g) vertex fires but a corresponding neuron in theP(u^(g)) vertex does not, this is a false positive. The neuron in theu^(g) vertex is trained to unlearn the false positive. If a neuron inthe u^(g) vertex does not fire but a corresponding neuron in theP(u^(g)) vertex does fire, this is a false negative. The neuron in theu^(g) vertex is trained to learn the false negative. Similarly, goodperception neurons in the v^(g) vertex are trained to approximate goodaction neurons in the P(v^(g)) vertex and not to approximate bad actionneurons in the P(v^(b)) vertex.

FIG. 20 illustrates an example of weights of the synaptic connectionsbetween neuron populations, in accordance with an embodiment of theinvention. The weight of the synaptic connections interconnecting theneurons in the v^(g) vertex to the neurons in the u^(g) vertex must bethe same as the weight of the synaptic connections interconnecting theneurons in the v^(b) vertex to the neurons in the u^(b) vertex.Similarly, the weight of the synaptic connections interconnecting theneurons in the P(u^(g)) vertex to the neurons in the P(v^(g)) vertexmust be the same as the weight of the synaptic connectionsinterconnecting the neurons in the P(u^(b)) vertex to the neurons in theP(v^(b)) vertex.

In one embodiment, the weight of the synaptic connectionsinterconnecting the neurons in the v^(g) vertex to the neurons in theu^(g) vertex is asymmetric to the weight of the synaptic connectionsinterconnecting the neurons in the P(u^(g)) vertex to the neurons in theP(v^(g)) vertex. Likewise, the weight of the synaptic connectionsinterconnecting the neurons in the v^(b) vertex to the neurons in theu^(b) vertex is asymmetric to the weight of the synaptic connectionsinterconnecting the neurons in the P(u^(b)) vertex to the neurons in theP(v^(b)) vertex.

FIG. 21 illustrates another example of weights of the synapticconnections between neuron populations, in accordance with an embodimentof the invention. In another embodiment, the weight of the synapticconnections interconnecting the neurons in the v^(g) vertex to theneurons in the u^(g) vertex is symmetric to the weight of the synapticconnections interconnecting the neurons in the P(u^(g)) vertex to theneurons in the P(v^(g)) vertex. Likewise, the weight of the synapticconnections interconnecting the neurons in the v^(b) vertex to theneurons in the u^(b) vertex is symmetric to the weight of the synapticconnections interconnecting the neurons in the P(u^(b)) vertex to theneurons in the P(v^(b)) vertex.

Symmetric weights are the preferred embodiment for the example providedin FIG. 19A. Symmetric or asymmetric weights may be used for the exampleprovided in FIG. 19B.

FIG. 22A illustrates an example Hebbian learning rule, in accordancewith the present invention. In one embodiment, the neurons 1 in theneural network 600 are spiking neurons. The Hebbian learning rule isapplied when a good neuron fires.

FIG. 22B illustrates an example anti-Hebbian learning rule, inaccordance with the present invention. The anti-Hebbian learning rule isapplied when a bad neuron fires.

FIG. 23 illustrates a flowchart of an example process 800 for a lattice,in accordance with an embodiment of the invention. In process block 801,establish first nodes and second nodes arranged in a lattice, whereineach second node is a union of two or more first nodes. In process block802, for each node, specify an acyclic digraph comprising verticesinterconnected via directed edges. In process block 803, interconnectnodes via bottom-up signaling pathways arranged in an acyclic bottom-updigraph, wherein bottom-up signaling pathways include one or morevertices and directed edges. In process block 804, interconnect nodesvia top-down signaling pathways arranged in an acyclic top-down digraph,wherein top-down signaling pathways include one or more vertices anddirected edges. In process block 805, provide directed edges thatinterconnect the bottom-up digraph to the top-down digraph.

FIG. 24 illustrates a flowchart of an example process 900 for a neuralnetwork, in accordance with an embodiment of the invention. In processblock 901, establish a neuron population for each vertex, wherein eachneuron population in the bottom-up digraph and top-down digraphcomprises perception neurons and action neurons, respectively. Inprocess block 902, designate perception neurons at an input periphery asinput neurons configured to receive sensory input, and designate actionneurons at an output periphery as output neurons configured to generatemotor output. In process block 903, the input neurons drive theperception neurons along bottom-up pathways, and the action neuronsalong the top-down pathways drive the output neurons. In process block904, each perception neuron along a bottom-up pathway is trained using alearning rule, based on a firing event of a corresponding action neuronalong a reciprocal top-down pathway, and each action neuron along atop-down pathway is trained using a learning rule, based on a firingevent of a corresponding perception neuron along a reciprocal bottom-uppathway.

FIG. 25 is a high level block diagram showing an information processingcircuit 300 useful for implementing one embodiment of the presentinvention. The computer system includes one or more processors, such asprocessor 302. The processor 302 is connected to a communicationinfrastructure 304 (e.g., a communications bus, cross-over bar, ornetwork).

The computer system can include a display interface 306 that forwardsgraphics, text, and other data from the communication infrastructure 304(or from a frame buffer not shown) for display on a display unit 308.The computer system also includes a main memory 310, preferably randomaccess memory (RAM), and may also include a secondary memory 312. Thesecondary memory 312 may include, for example, a hard disk drive 314and/or a removable storage drive 316, representing, for example, afloppy disk drive, a magnetic tape drive, or an optical disk drive. Theremovable storage drive 316 reads from and/or writes to a removablestorage unit 318 in a manner well known to those having ordinary skillin the art. Removable storage unit 318 represents, for example, a floppydisk, a compact disc, a magnetic tape, or an optical disk, etc. which isread by and written to by removable storage drive 316. As will beappreciated, the removable storage unit 318 includes a computer readablemedium having stored therein computer software and/or data.

In alternative embodiments, the secondary memory 312 may include othersimilar means for allowing computer programs or other instructions to beloaded into the computer system. Such means may include, for example, aremovable storage unit 320 and an interface 322. Examples of such meansmay include a program package and package interface (such as that foundin video game devices), a removable memory chip (such as an EPROM, orPROM) and associated socket, and other removable storage units 320 andinterfaces 322 which allow software and data to be transferred from theremovable storage unit 320 to the computer system.

The computer system may also include a communication interface 324.Communication interface 324 allows software and data to be transferredbetween the computer system and external devices. Examples ofcommunication interface 324 may include a modem, a network interface(such as an Ethernet card), a communication port, or a PCMCIA slot andcard, etc. Software and data transferred via communication interface 324are in the form of signals which may be, for example, electronic,electromagnetic, optical, or other signals capable of being received bycommunication interface 324. These signals are provided to communicationinterface 324 via a communication path (i.e., channel) 326. Thiscommunication path 326 carries signals and may be implemented using wireor cable, fiber optics, a phone line, a cellular phone link, an RF link,and/or other communication channels.

In this document, the terms “computer program medium,” “computer usablemedium,” and “computer readable medium” are used to generally refer tomedia such as main memory 310 and secondary memory 312, removablestorage drive 316, and a hard disk installed in hard disk drive 314.

Computer programs (also called computer control logic) are stored inmain memory 310 and/or secondary memory 312. Computer programs may alsobe received via communication interface 324. Such computer programs,when run, enable the computer system to perform the features of thepresent invention as discussed herein. In particular, the computerprograms, when run, enable the processor 302 to perform the features ofthe computer system. Accordingly, such computer programs representcontrollers of the computer system.

From the above description, it can be seen that the present inventionprovides a system, computer program product, and method for implementingthe embodiments of the invention. References in the claims to an elementin the singular is not intended to mean “one and only” unless explicitlyso stated, but rather “one or more.” All structural and functionalequivalents to the elements of the above-described exemplary embodimentthat are currently known or later come to be known to those of ordinaryskill in the art are intended to be encompassed by the present claims.No claim element herein is to be construed under the provisions of 35U.S.C. section 112, sixth paragraph, unless the element is expresslyrecited using the phrase “means for” or “step for.”

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

What is claimed is:
 1. A method, comprising: interconnecting a pluralityof neural nodes via an interconnect network of multiple signalingpathways arranged in a lattice; wherein interconnecting said pluralityof neural nodes includes connecting a plurality of first nodes in afirst set of nodes with a plurality of second nodes in a second set ofnodes; each node generating a signal in response to input signalsreceived from one or more other nodes via the interconnect network; anda connected node in the second set exchanging signals with at least twonodes in the first set via the interconnect network.
 2. The method ofclaim 1, wherein a node comprises one or more neuron populationsinterconnected via multiple directed edges arranged in an acyclicdigraph, wherein each neuron population comprises one or more neurons,and each edge includes a signaling pathway in the interconnect network.3. The method of claim 2, wherein interconnecting said plurality ofneural nodes further includes interconnecting said plurality of neuralnodes via bottom-up signaling pathways arranged in an acyclic bottom-updigraph in the interconnect network, each bottom-up signaling pathwayincluding one or more neuron populations and directed edges.
 4. Themethod of claim 3, wherein interconnecting said plurality of neuralnodes further includes interconnecting said plurality of neural nodesvia top-down signaling pathways arranged in an acyclic top-down digraphin the interconnect network, each top-down signaling pathway includingone or more neuron populations and directed edges.
 5. The method ofclaim 4, wherein: each neuron population in the top-down digraphcorresponds to a neuron population in the bottom-up digraph; and eachtop-down signaling pathway in the top-down digraph has a reciprocalbottom-up signaling pathway in the bottom-up digraph, such thatinformation flows along said top-down signaling pathway in a firstdirection, and information flows along said reciprocal bottom-upsignaling pathway in a direction opposite of the first direction.
 6. Themethod of claim 5, further comprising: designating a neuron populationat an input periphery of the neural network as an input neuronpopulation configured to receive sensory input, wherein the input neuronpopulation drives neurons along a number of bottom-up signalingpathways; a first set of neurons along bottom-up signaling pathwaysdriving a first set of neurons along top-down signaling pathways; anddesignating a neuron population at an output periphery of the neuralnetwork as an output neuron population configured to generate motoroutput, wherein neurons along a number of top-down signaling pathwaysdrive the output neuron population.
 7. The method of claim 6, furthercomprising: training each neuron along a bottom-up signaling pathwayusing a learning rule based on the firing events of said neuron and thefiring events of the corresponding neuron along a reciprocal top-downsignaling pathway; and training each neuron along a top-down signalingpathway using a learning rule based on the firing events of said neuronand the firing events of the corresponding neuron along a reciprocalbottom-up signaling pathway.